Describe — 5 marks
A student is investigating the motion of a toy car rolling down a ramp. They measure the distance travelled and the time taken, and need to rearrange equations to find the car's acceleration. The relationship between distance (s), initial velocity (u), acceleration (a), and time (t) is given by the equation: s = ut + ½at²
-
Describe the first step needed to rearrange the equation s = ut + ½at² to make a the subject.
[2 marks]
-
The student measures s = 2.0 m, u = 0 m/s, and t = 2.0 s. Describe how you would use these values and the rearranged equation to find the acceleration of the car.
[2 marks]
-
Describe why it is important to rearrange equations correctly when solving physics problems.
[1 mark]
Show mark scheme
Define — 2 marks
A student is investigating the motion of a toy car rolling down a ramp. They measure the distance travelled and the time taken, and need to rearrange equations to find the car's acceleration.
-
Define what is meant by the term 'acceleration'.
[1 mark]
-
The equation for acceleration is a = (v - u) / t. Rearrange this equation to make v the subject.
[1 mark]
Show mark scheme
- The rate of change of velocity / change in velocity per unit time (accept: how quickly velocity changes)
- v = u + at (accept equivalent forms showing correct rearrangement)
Explain — 4 marks
A student is investigating the motion of a toy car rolling down a ramp. They measure the distance travelled and the time taken. To find the average speed, they need to rearrange and use the equation: distance = speed × time, or d = s × t
-
The equation for distance is d = s × t, where d is distance in metres, s is speed in m/s, and t is time in seconds. Rearrange this equation to make speed (s) the subject.
[1 mark]
-
The toy car travels 2.4 metres in 3 seconds down the ramp. Use your rearranged equation from part (a) to calculate the average speed of the car. Show your working.
[2 marks]
-
Explain why it is important to rearrange the equation before substituting numerical values into it.
[1 mark]
Show mark scheme
- Correctly rearranges to s = d / t or s = d ÷ t (1 mark)
- Correctly substitutes values: s = 2.4 / 3 or s = 2.4 ÷ 3 (1 mark)
- Correct final answer: s = 0.8 m/s (1 mark)
- Explains that rearranging ensures the unknown quantity is isolated / makes the calculation clearer / avoids confusion about which value to divide or multiply (1 mark)
Define — 3 marks
A student is investigating the motion of a trolley down a ramp. They measure the distance travelled and time taken, and need to rearrange kinematic equations to find acceleration. The equation they are working with is: s = ut + ½at², where s is displacement, u is initial velocity, t is time, and a is acceleration.
-
Define what is meant by the term 'displacement' and explain how it differs from 'distance travelled'.
[1 mark]
-
Rearrange the equation s = ut + ½at² to make acceleration (a) the subject. Show all steps in your working.
[1 mark]
-
The student measures s = 2.5 m, u = 0.2 m/s, and t = 2.0 s. Using your rearranged equation from part (b), calculate the acceleration of the trolley. Give your answer to 2 significant figures.
[1 mark]
Show mark scheme
Calculate — 2 marks
A rectangular picture frame has sides of length (2x + 3) cm and (x + 4) cm.
-
(01.1) Write an expression for the perimeter of the picture frame.
[1 mark]
-
(01.2) Simplify your expression fully.
[1 mark]
Show mark scheme
- (01.1) Correct expression for perimeter, e.g. 2(2x + 3) + 2(x + 4) or (2x + 3) + (x + 4) + (2x + 3) + (x + 4)
- (01.2) 6x + 14 oe
GCSE Perfect